The subject invention relates generally to a novel concept and device employing elastomers as the mechanism for damping the vibrations of structures subject to vibration.
The best known and commercially successful seismic device for damping overhead conductors is the Stockbridge damper. Such a damper comprises a stranded steel cable, two weights attached respectively to the ends of the cable and a conductor clamp attached to the cable at a location intermediate the weights. With vibration of the conductor, the inertia of the weights causes working of the cable such that friction between the strands of the cable dissipates the energy of vibration to the surrounding atmosphere in the form of heat. The Stockbridge damper has two resonant modes of motion, with each mode combining rotation and vertical translation of the weight in differing proportions.
In U.S. Pat. No. 3,478,160 to Reed, a single elastomer bushing is employed to support a mass from an overhead conductor in a manner that locates the center of gravity of the mass in three mutually orthogonal planes that are offset from the center of suspension of the mass. Such a device provides "coupled" modes of vibration that offer damping at different frequencies of vibration of an overhead conductor.
In designing the damper of the subject invention, approximations of seismic mass, radius of gyration of the mass, the location of the center of gravity of the mass and certain other dimensions were determined by computer simulation. The simulation indicated that the dimensions of a good damping device required a certain spring constant for both vertical and horizontal translation of the mass with respect to its supporting clamp as well as a certain rotational spring constant. When these several spring constants were sought in a practical construction, it was found that they could not be obtained simultaneously except in a very singular configuration.
It should be understood that damping elastomers were intended for use as the spring-like elements of the subject invention because such materials incorporate sufficient hysteresis in their characteristics that no other source of energy dissipation is needed. These materials also lend themselves to easy and economical fabrication in any desired shape. However, the damping capabilities of elastomers are greatest when they are deflected in shear rather than extension, such that they are best applied in the form of pads that couple bodies at opposed and parallel surfaces of said bodies, the surfaces being chosen such that the relative motions between them that occur during vibratory service induce only shearing of the pads, and not compression, extension or rocking. The pads are of uniform thickness to fill the space between the opposed and parallel surfaces, but their cross-sectional shapes (in planes parallel to those surfaces) are generally not restricted by considerations of damping effectiveness. Shapes that are easy to fabricate are ordinarily employed. For example, the elastomer pads used for suspending the engines in many cars are square or rectangular in cross section.
It should also be understood that where the spring constant and strength of an elastomer pad are important, choices and compromises may be made among (1) the elastomer composition, (2) the thickness of the pad and (3) the cross-sectional area of the pad. The multiplicity of options available generally assures that a small number of required characteristics (spring constant and strength) can be satisfactorily provided. This ease of achieving a desired combination of characteristics was not forthcoming in the selection of pads for the subject invention, however. The requirement that the rotational spring constant of the elastomer suspension have a certain value or, more exactly, have a certain ratio to the translational spring constant, severely restricted the choice as to the configuration of the elastomer pads.
The restriction reflected the conflict between three requirements. The first was the requirement that the ratio of rotational to translational spring constants have a certain value. Now this ratio is equal in practice to the mean-square radius of the pad's cross section. For example, if the pad takes the form of a thin ring of a certain radius, then the ratio of rotational to translational spring constants is the square of that radius. For cross sections having other shapes, the calculation of mean-square radius is more complicated, but mathematical tables exist that provide such information for many shapes.
The second requirement contributing to the conflict had to do with the strength of the pads. Two types of strength were of concern. One was the strength with respect to the vibratory motions the damper would experience. These movements would subject the pad to shearing and could lead to tearing or of fatigue of the elastomer were the shear strains in the elastomer too great. These strains can be minimized by using pads of generous thickness so that the relative movements of the opposed parallel surfaces can be absorbed by a large thickness of elastomer material. The other strength requirement becomes of concern when the pad is of such great thickness, but small cross section, that it may be considered to be a column or a wall subject to buckling. The most convenient means of assembly for the dampers of the invention is often to compress them together in the form of a sandwich with the pads held in place by compression, as will be discussed below. The likelihood of buckling the pads may be minimized by using pads of generally squat shape.
These two strength aspects in combination lead to use of pads that are thick and squat, that is, with diameter equal to or greater than, say, half the thickness. The requirement for a certain rotational to translational spring constant ratio means that this diameter must exceed twice the square root of that ratio.
The third requirement contributing to the conflict was the fact that elastomers having desirable properties over a broad enough range of temperatures to make them suitable for use on transmission lines also were fairly stiff, that is, they had fairly high modulus of shear. The effect of this was that pads with great enough diameter to satisfy spring constant ratio requirements and small enough in thickness to be considered squat were also much too stiff.
Consideration was given to configuring the pad as a ring so as to reduce its stiffness by reducing the area of the pad. The ratio of spring constants could then be preserved by giving the ring a radius equal to the square root of the ratio of natural frequencies. When the area was sufficiently reduced using this procedure, however, the wall thickness of the ring (in the radial direction) became small compared with the pad thickness, and the danger arose of wall collapse occurring similar to what happens when one steps on the end of a beverage can. It was this combination of constraints that comprised the problem which the present invention addresses.
The severity of the problem was aggravated by the fact that practical design militates in favor of utilizing not one but two pads in the damper so that the inertial mass may be fabricated in two halves which on assembly embrace between them the two elastomer pads which in turn embrace between them a tongue, extension or arm of the conductor-engaging clamp. In such a structure, doubling the number of pads doubles the effective spring constants of the elastomer suspension because the pads act mechanically in parallel. To regain the spring constants afforded by a single pad, it is necessary to double the thickness of each of the two pads thus making their walls even more prone to buckling.